An interferential measuring system for measuring in two directions is described by Fromund Hock of Stuttgart, Germany, in Section 11.6 of his 1978 dissertation entitled "Photoelektrische Messung der Anderung yon Langen oder Winkelpositionen mir Hilfe yon Beugungsgittern" [Photo-Electrical Measurement of the Changes in Lengths and Angular Position with the Aid of Diffraction Gratings]. A collimated light beam emitted by a light source penetrates a grating of a scale extending diagonally to the two directions of measurement as well as four locality frequency filter screens and is imaged by means of two lenses on a first linear grating which is aligned in the first measuring direction and combines the diffracted bundle of light beams which had been diffracted into this first measuring direction at the scale. The combined diffracted bundles of beams of the first measuring direction are guided by means of a third lens to first detectors which provide scanning signals for the generation of measuring values for the first measuring direction. The diffracted bundles of beams which had been diffracted into the second measuring direction at the scale are imaged by means of a fourth lens on a second linear grating which is aligned in the second measuring direction and then reach second detectors providing scanning signals for the generation of measuring values for the second measuring direction. A disadvantage associated with such a measuring system is its elaborate and complex construction.